List of mathematical properties of points
# List of mathematical properties of points

In mathematics, the following appear:

* Algebraic point
* Associated point
* Base point
* Closed point
* Divisor point
* Embedded point
* Extreme point
* Fermat point
* Fixed point
* Focal point
* Geometric point
* Hyperbolic equilibrium point
* Ideal point
* Inflection point
* Integral point
* Isolated point
* Generic point
* Heegner point
* Lattice hole, Lattice point
* Lebesgue point
* Midpoint
* Napoleon points
* Non-singular point
* Normal point
* Parshin point
* Periodic point
* Pinch point
* Point (geometry)
* Point source
* Rational point
* Recurrent point
* Regular point, Regular singular point
* Saddle point
* Semistable point
* Separable point
* Simple point
* Singular point of a curve
* Singular point of an algebraic variety
* Smooth point
* Special point
* Stable point
* Torsion point
* Vertex (curve)
* Weierstrass point

## Calculus

* Critical point (aka stationary point), any value v in the domain of a differentiable function of any real or complex variable, such that the derivative of v is 0 or undefined

## Geometry

* Antipodal point, the point diametrically opposite to another point on a sphere, such that a line drawn between them passes through the centre of the sphere and forms a true diameter
* Conjugate point, any point that can almost be joined to another by a 1-parameter family of geodesics (e.g., the antipodes of a sphere, which are linkable by any meridian
* Vertex (geometry), a point that describes a corner or intersection of a geometric shape
   * Apex (geometry), the vertex that is in some sense the highest of the figure to which it belongs

## Topology

* Adherent point, a point x in topological space X such that every open set containing x contains at least one point of a subset A
* Condensation point, any point p of a subset S of a topological space, such that every open neighbourhood of p contains uncountably many points of S
* Limit point, a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be approximated by points of S, since every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself
   * Accumulation point (or cluster point), a point x ∈ X of a sequence $(x_n)_{n∈N}$ for which there are, for every neighbourhood V of x, infinitely many natural numbers n such that $x_n$ ∈ V
